In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-...In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.展开更多
目的探讨气管切开术后不同痰液黏稠度患者所需的气道湿化量。方法随机选取气管切开术后患者74例,共270例次,根据痰液黏稠度不同分为Ⅰ度、Ⅱ度、Ⅲ度三组,每组按不同气道湿化剂量分为三个亚组。于24h观察气道湿化变化趋势,48 h根据痰液...目的探讨气管切开术后不同痰液黏稠度患者所需的气道湿化量。方法随机选取气管切开术后患者74例,共270例次,根据痰液黏稠度不同分为Ⅰ度、Ⅱ度、Ⅲ度三组,每组按不同气道湿化剂量分为三个亚组。于24h观察气道湿化变化趋势,48 h根据痰液黏稠度分级标准评判湿化结果,采用χ2检验进行统计学分析。结果Ⅰ度、Ⅱ度、Ⅲ度患者48 h适合的气道湿化量分别为6 m l/h、12 m l/h、16 m l/h。结论不同痰液黏稠度患者应给予不同的气道湿化剂量。展开更多
文摘In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.
文摘目的探讨气管切开术后不同痰液黏稠度患者所需的气道湿化量。方法随机选取气管切开术后患者74例,共270例次,根据痰液黏稠度不同分为Ⅰ度、Ⅱ度、Ⅲ度三组,每组按不同气道湿化剂量分为三个亚组。于24h观察气道湿化变化趋势,48 h根据痰液黏稠度分级标准评判湿化结果,采用χ2检验进行统计学分析。结果Ⅰ度、Ⅱ度、Ⅲ度患者48 h适合的气道湿化量分别为6 m l/h、12 m l/h、16 m l/h。结论不同痰液黏稠度患者应给予不同的气道湿化剂量。
